Final answer:
The algebraic expression for the time to travel 100 miles at an average speed of r miles per hour is 100/r, from the formula time = distance/speed.
Step-by-step explanation:
The algebraic expression that represents the time (in hours) to travel 100 miles at an average speed of r miles per hour is given by the expression 100/r. This expression comes from the formula for time, which is time = distance/speed. In this case, the distance is 100 miles and the speed is r miles per hour, so plugging these values into the formula yields the expression 100/r. It's derived from the basic formula for time, where time equals distance divided by speed. In this instance, the expression encapsulates the notion that as the speed increases, the time required for the journey decreases, and vice versa.